In a villa surrounded by flowers, Mirina was reading Lucian's paper using the unit circle to prove the compatibility of Tower Geometry with Levsky Geometry. Once again, she was struck by the beauty of mathematics. After a long while, she finally picked up her pen and wrote:
"A brilliant conception, a concise demonstration — it fully reveals the beauty of mathematics while simultaneously proving the compatibility of Levsky's new geometry with Tower Geometry. It irrefutably establishes the new geometric system, overturning the mathematical world constructed from real-world experience and intuitive understanding, and illuminating another path for mathematical development and proof."
"This paper holds a position of considerable importance in establishing the validity of the new geometric system. The mathematical thought it embodies is well worth our exploration and possesses a degree of pioneering significance. Recommended reward: forty Arcane Points, five hundred Magic Score."
Mirina evaluated it strictly according to the review criteria, not allowing her personal preferences to influence the outcome. Had she done so, as an authority in the mathematical and physical sciences and as a mathematician herself, she would undoubtedly have given a higher rating and a more generous reward to a paper brimming with such mathematical beauty.
…………
At almost the same time, Salgueiro was also reviewing Lucian's "An Attempt to Explain Non-Tower Geometry":
"The paper presents a mathematical model that defies intuitive understanding yet genuinely exists, making a groundbreaking contribution to proving the validity of Levsky Geometry. It makes us truly realize that this is indeed an entirely new geometric system fundamentally different from Tower Geometry."
"Given the groundbreaking contribution of this mathematical model and proof process to the new field of geometry, its highly significant position, and the fact that it contains content well worth discussion and research, recommended reward: sixty Arcane Points, six hundred Magic Score."
Only when he set down his pen did Salgueiro realize that the dark night of winter had already descended. Outside, the wind howled and everything was pitch black. Yet from within that frigid darkness, he seemed to glimpse a sliver of light — a light for the future development of the mathematical sciences.
"If this new geometric system holds genuine arcane significance..."
"Evans's ideas about axiomatization seem rather interesting..."
…………
A week later, in the morning, Samantha came to the Tower as usual to study under her teacher.
"Good morning, Lady Samantha." Several low-ranking Archanists who were acquainted with her greeted her one after another as she arrived.
Inside the great hall, the vaulted dome was cloaked in deep darkness, studded with arcane crystal lamps arranged to illuminate the space. They were distributed according to different galaxies and constellations, resembling a vast star chart.
Samantha nodded with a serious but not impolite acknowledgment, then asked with a trace of puzzlement: "Leo, Gina — what are you doing here so early?"
As far as she knew, the teacher of these low-ranking Archanists — her friend, Fourth-level Archanist and Fifth-ring Diviner Dacera — never instructed students on Fridays. And at this hour, the laboratories and library within the Tower were not yet open, so there was no need to arrive so early.
"Lady Samantha, didn't you hear? The Tower issued a notice yesterday — a new journal is being released today. We're all curious, so we came early to wait." The round-faced, adorable Gina answered earnestly.
Samantha had spent the past two days sleeping through the day and staying up at night observing the stars in order to improve one of her new spells, so she had taken leave from the Tower and naturally had not heard about this. At this moment, her expression shifted almost imperceptibly, and she murmured to herself: "A new journal — Lucian? The one with Evans's foreword?"
"I don't know." Leo, the chubby little fellow who hadn't yet reached twenty-five but was already putting on weight, shook his head blankly. Lady Samantha seemed to know more than they did.
"Hey, Samantha — you're here to buy Natural Philosophy too?" Rachel's bright, lively greeting came from behind Samantha. She was always brimming with youthful vitality, radiating sunshine, the kind of person whose presence automatically lifted your spirits.
Samantha allowed herself a rare smile: "You too?" The two had completely opposite personalities but were close friends.
Rachel sighed deliberately: "Yes. As a member of the Arcane Review Committee and a senior figure in the Tower, my teacher Lady Isabella should have received a complimentary copy. But she's out exploring, searching for new illusion-materials, so I have no choice but to come buy it myself, the poor thing."
In Rachel's presence, Gina and the others were noticeably more respectful. First, they were not well acquainted with her. Second, Rachel was a laureate of the Witch's Crown — the crystal-clear hair clip currently adorning her flaxen hair was particularly awe-inspiring to them.
"Do you know the contents of Natural Philosophy, the foreword?" Samantha asked instinctively. Otherwise, there was no reason for Rachel to come to the Tower this early. With her status and standing, would she really worry about not being able to obtain a copy?
Rachel looked at Samantha in puzzlement: "No, but as the inaugural issue of a journal, think of how collectible and commemorative it is — especially one you purchase with your own hands."
"..." Samantha realized she had forgotten her friend's collecting obsession.
At that moment, the Tower library behind the reception desk opened, and two female Magic Apprentices on reception duty carried out several thick stacks of black-bound books.
"Let me see what direction this companion journal to Star Charts is taking." Rachel tugged Samantha briskly toward the reception desk, her voice bright with curiosity.
Samantha wore a thoughtful expression: "It should be related to mathematics?" This was something her teacher Neseeka had mentioned in passing. Moreover, when helping her teacher return the review results, she had already seen Lucian's — Evans's — new geometry paper. At the time, those counter-intuitive, bewildering propositions had made her head throb. She had instinctively recoiled and nearly failed to understand it.
But soon enough, she was shaken by the mathematical model provided afterward. She returned to read the paper carefully once more, and found herself simultaneously rejecting it from the depths of her heart while being persuaded by its rigorous, self-consistent logic and elegant model. It gave her an experience akin to a cerebral tremor from having the very foundations of her worldview shaken, leaving her in a state of dazed contradiction. It took two or three days before she recovered, finally beginning to accept the fact that the new geometric system truly existed.